Student/VectorCalculus/GetSpace - Maple Help

Student[VectorCalculus]

 GetSpace
 returns the vector space attribute of a rooted Vector

 Calling Sequence GetSpace(v)

Parameters

 v - Vector; a rooted Vector

Description

 • The call GetSpace(v) returns a module which encodes the vector space to which the rooted Vector v belongs.
 • The Student[VectorCalculus] package uses the same Vector data structures as the VectorCalculus package. For details about the various types of Vectors in these packages, see VectorCalculus,Details.
 • For details about the representation of vector spaces, see Student[VectorCalculus][VectorSpace].

Examples

 > $\mathrm{with}\left(\mathrm{Student}\left[\mathrm{VectorCalculus}\right]\right):$
 > $f≔\mathrm{Vector}\left(\left[1,t\right],\mathrm{coords}=\mathrm{polar}\left[r,\mathrm{\theta }\right]\right)$
 ${f}{≔}\left({1}\right){{e}}_{{r}}{+}\left({t}\right){{e}}_{{\mathrm{θ}}}$ (1)
 > $v≔\mathrm{simplify}\left(\mathrm{TangentVector}\left(f\right)\right)$
 ${v}{≔}\left[\begin{array}{c}{0}\\ {1}\end{array}\right]$ (2)
 > $\mathrm{vs}≔\mathrm{GetSpace}\left(v\right)$
 ${\mathrm{vs}}{≔}{\mathbf{module}}\left({}\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathbf{local}}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathrm{_origin}}{,}{\mathrm{_coords}}{,}{\mathrm{_coords_dim}}{;}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathbf{export}}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathrm{GetCoordinates}}{,}{\mathrm{GetRootPoint}}{,}{\mathrm{Vector}}{,}{\mathrm{eval}}{;}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathbf{end module}}$ (3)
 > $\mathrm{vs}:-\mathrm{GetCoordinates}\left(\right)$
 ${{\mathrm{polar}}}_{{r}{,}{\mathrm{\theta }}}$ (4)
 > $\mathrm{vs}:-\mathrm{GetRootPoint}\left(\right)$
 $\left(\sqrt{{{\mathrm{cos}}{}\left({t}\right)}^{{2}}{+}{{\mathrm{sin}}{}\left({t}\right)}^{{2}}}\right){{e}}_{{r}}{+}\left({\mathrm{arctan}}{}\left({\mathrm{sin}}{}\left({t}\right){,}{\mathrm{cos}}{}\left({t}\right)\right)\right){{e}}_{{\mathrm{θ}}}$ (5)